Ionizing radiation is a known and well-quantified human cancer risk factor, based on a remarkably consistent body of information from epidemiological studies of exposed populations. Typical examples of risk estimation include use of Japanese atomic bomb survivor data to estimate future risk from radiation-related cancer among American patients receiving multiple computed tomography scans, persons affected by radioactive fallout, or persons whose livelihoods involve some radiation exposure, such as x-ray technicians, interventional radiologists, or shipyard workers. Our estimates of radiation-related risk are uncertain, reflecting statistical variation and our imperfect understanding of crucial assumptions that must be made if we are to apply existing epidemiological data to particular situations. Fortunately, that uncertainty is also highly quantifiable, and can be presented concisely and transparently. Radiation protection is ultimately a political process that involves consent by stakeholders, a diverse group that includes people who might be expected to be risk-averse and concerned with plausible upper limits on risk (how bad could it be?), cost-averse and concerned with lower limits on risk (can you prove there is a nontrivial risk at current dose levels?), or combining both points of view. How radiation-related risk is viewed by individuals and population subgroups also depends very much on perception of related benefit, which might be (for example) medical, economic, altruistic, or nonexistent. The following presentation follows the lead of National Council on Radiation Protection and Measurements (NCRP) Commentary 14, NCRP Report 126, and later documents in treating radiation protection from the viewpoint of quantitative uncertainty analysis.